Khan.scratchpad.disable(); For every level Vanessa completes in her favorite game, she earns $520$ points. Vanessa already has $460$ points in the game and wants to end up with at least $2140$ points before she goes to bed. What is the minimum number of complete levels that Vanessa needs to complete to reach her goal?
To solve this, let's set up an expression to show how many points Vanessa will have after each level. Number of points $=$ $ $ Levels completed $\times$ Points per level $+$ Starting points Since Vanessa wants to have at least $2140$ points before going to bed, we can set up an inequality. Number of points $\geq 2140$ Levels completed $\times$ Points per level $+$ Starting points $\geq 2140$ We are solving for the number of levels to be completed, so let the number of levels be represented by the variable $x$ We can now plug in: $x \cdot 520 + 460 \geq 2140$ $ x \cdot 520 \geq 2140 - 460 $ $ x \cdot 520 \geq 1680 $ $x \geq \dfrac{1680}{520} \approx 3.23$ Since Vanessa won't get points unless she completes the entire level, we round $3.23$ up to $4$ Vanessa must complete at least 4 levels.